WORKED PROBLEMS

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WORKED PROBLEMS

Problem 1

The percentage of cytosine in a double-stranded DNA molecule is 40%. What is the percentage of thymine?

Solution Strategy

What information is required in your answer to the problem?

The percentage of thymine in the DNA molecule.

What information is provided to solve the problem?

  • The DNA molecule is double-stranded.

  • The percentage of cytosine is 40%.

For help with this problem, review:

The Primary Structure of DNA and Secondary Structures of DNA in Section 8.3.

Recall: In double-stranded DNA, A pairs with T, whereas G pairs with C; so the percentage of A equals the percentage of T, and the percentage of G equals the percentage of C.

Solution Steps

If C = 40%, then G also must be 40%. The total percentage of C + G is therefore 40% + 40% = 80%. All the remaining bases must be either A or T; so the total percentage of A + T = 100% − 80% = 20%; because the percentage of A equals the percentage of T, the percentage of T is 20%/2 = 10%.

Problem 2

Which of the following relations will be true for the percentage of bases in double-stranded DNA?

  1. C + T = A + G

  2. C//A = T//G

Solution Strategy

What information is required in your answer to the problem?

Indicate whether C + T = A + G and C//A = T//G are true.

What information is provided to solve the problem?

  • The DNA is double-stranded.

  • Ratios of different groups of bases.

For help with this problem, review:

The Primary Structure of DNA and Secondary Structures of DNA in Section 8.3.

Solution Steps

An easy way to determine whether the relations are true is to arbitrarily assign percentages to the bases, remembering that, in double-stranded DNA, A = T and G = C. For example, if the percentages of A and T are each 30%, then the percentages of G and C are each 20%. We can substitute these values into the equations to see if the relations are true.

  1. 20 + 30 = 30 + 20. This relation is true.

  2. 20//30 ≠ 30//20. This relation is not true.

Problem 3

A diploid plant cell contains 2 billion base pairs of DNA.

  1. How many nucleosomes are present in the cell?

  2. Give the number of molecules of each type of histone protein associated with the genomic DNA.

Solution Strategy

What information is required in your answer to the problem?

The number of nucleosomes per cell and the numbers of each type of histone protein associated with the DNA.

What information is provided to solve the problem?

  • The cell contains 2 billion base pairs of DNA.

For help with this problem, review:

Recall: The repeating unit of the chromosome is a nucleosome, which consists of DNA complexed with histone proteins.

The Nucleosome in Section 8.4.

Solution Steps

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Each nucleosome encompasses about 200 bp of DNA: 145–147 bp of DNA wrapped around the histone core, 20–22 bp of DNA associated with the H1 protein, and another 30–40 bp of linker DNA.

  1. To determine how many nucleosomes are present in the cell, we simply divide the total number of base pairs of DNA (2 × 109 bp) by the number of base pairs per nucleosome:

    2 × 109 nucleotides//2 × 102 nucleotides per nucleosome = 1 × 107 nucleosomes

    Thus, there are approximately 10 million nucleosomes in the cell.

  2. Each nucleosome includes two molecules each of H2A, H2B, H3, and H4 histones. Therefore, there are 2 × 107 molecules each of H2A, H2B, H3, and H4 histones. Each nucleosome has associated with it one copy of the H1 histone, so there are 1 × 107 molecules of H1.